This paper introduces Signal Theory, a framework that integrates seven foundational traditions into a single architecture for optimal communication. It defines the Signal as the fundamental unit of actionable communication — a formal 5-tuple S = (M, G, T, F, W) classified across five dimensions: Mode (sensory channel), Genre (conventionalized form), Type (communicative function), Format (container), and Structure (internal skeleton). The framework is organized around one root metric — Signal-to-Noise Ratio — and four governing principles that define the constraints on its maximization: channel capacity (Shannon, 1948), requisite variety (Ashby, 1956), recursive viable architecture (Beer, 1972), and closed-loop feedback (Wiener, 1948). Three additional traditions complete the classification system: speech genres (Bakhtin, 1986), illocutionary acts (Searle, 1976), and multimodal semiotics (Kress & van Leeuwen, 2001). Central contributions include: (1) a formal definition of the Signal as the fundamental unit of actionable communication; (2) the Optimal System — a cybernetic architecture satisfying all four governing constraints simultaneously at every level of recursion; (3) the Path of Least Resistance — showing that optimal encoding converges on the minimum-effort path through noise; (4) a unified taxonomy resolving naming failures across disciplines; (5) eleven formally defined failure modes with diagnostic questions and corrective actions; and (6) integration of Machine Intelligence as Signal Processors within the same architecture. The framework is technology-independent and applies recursively from a single message to an entire organization. Four companion documents extend the theory into applied specifications.